1. Field of the Invention
This invention relates to a phase modulated fiber-optic gyroscope.
2. Prior Art
The fiber-optic gyroscope is an apparatus for measuring the angular velocity of a moving object. Monochromatic light is launched at opposite ends of a coil of many turns of a single-mode optical fiber and is transmitted clockwise and counterclockwise simultaneously, with the light emerging from one end of the coil interfering with the light emerging from the other end. If the fiber-optic coil is rotating about its own axis, a phase difference appears between the two light beams. Since this phase difference is proportional to the angular velocity of the rotation, one can determine the angular velocity of the rotation from the phase difference.
If the phase difference and angular velocity are written as .DELTA..theta. and .OMEGA., respectively, the following relationship holds: ##EQU1## where L is the fiber length of the sensor coil, a is the coil diameter, c is the speed of the light in a vacuum and .lambda. is the wavelength of the light in a vacuum. This effect is called the Sagnac effect and is well known.
In practice, however, it is not easy to detect the phase difference .DELTA..theta. because it contains non-rotational offsets inherent in the optical system. These offsets are subject to significant variations due to temperature changes. A further problem is that the output of a light-receiving device appears in the form of (1+cos.DELTA..theta.) in a fiber-optic gyroscope of the most primitive design. This results in low sensitivity and failure to detect the direction of rotation if .DELTA..theta. is small.
To cope with these difficulties, three different types of fiber-optic gyroscopes have been proposed, which operate on the principles of frequency modulation, phase modulation and phase shift, respectively. The present invention relates to a fiber-optic gyroscope that operates on the principle of phase modulation.
The basic construction of a phase modulated fiber-optic gyroscope is described below with reference to FIG. 1. Phase modulation is produced from a piezoelectric device around which one end portion of the optical fiber cable in the sensor coil is wound. By picking up the first-order term of the modulated wave, the phase difference can be determined in the form of sin.DELTA..theta..
Coherent light issuing from a light-emitting device 1 is split into two beams by a beam splitter 2. One of the two beams is converged by a coupling lens 4 and launched into end A of an optical fiber cable 5. This beam is transmitted through the sensor coil 6 counterclockwise. The other beam is converged by a coupling lens 3, launched into end B of the optical fiber 5 and transmitted through the sensor coil 6 clockwise.
The greater part of the optical fiber cable 5 forms the sensor coil 6 and only the part close to end B is wound around the piezoelectric device to form a phase modulation device 7.
An oscillator 10 produces an oscillating voltage that causes the piezoelectric device to expand or contract. The phase modulating part 8 of the optical fiber cable is wound onto the piezoelectric device, so it will expand or contract together with the piezoelectric device to produce a light signal containing a modulated component.
The light beam transmitted clockwise through the phase modulating part 8 and the sensor coil 6 will emerge from end A, and the other beam transmitted counterclockwise through the sensor coil 6 and the phase modulating part 8 will emerge at end B. The emerging light beams are recombined by the beam splitter 2 and launched as a single beam into a light-receiving device 9, which performs square-law detection on the light of interference.
Since the phase modulation device 7 is located asymmetrically with respect to the fiber-optic cable 5, the light being transmitted clockwise is phase-modulated at a slightly different time than the light being transmitted counterclockwise. The time, .tau., required for the light to pass through the sensor coil 6 is given by: ##EQU2## where L is the fiber length of the sensor coil 6 and n is the refractive index of the fiber core. If the phase modulation device 7 is positioned close to end B, the light being transmitted clockwise will be first phase-modulated before it is launched into the sensor coil 6. On the other hand, the light being transmitted counterclockwise passes through the sensor coil 6 before it is launched into the phase modulation device 7.
Let us write .OMEGA. for the angular frequency of a modulating signal. Since the difference in time between the phase modulation caused by the device 7 and the launching of the light into the light-receiving device 9 is .tau., the phase difference, .phi., of the modulation signal contained in the light of interference is given by: EQU .phi.=.OMEGA..tau. (3)
As described above, the Sagnac effect introduces a phase difference of .DELTA..theta. between the light transmitted clockwise and the light transmitted counterclockwise, and the phase modulation applied on the two light beams creates an additional phase difference of .phi. in the phase-modulated portion.
If the amplitude due to the action of the phase modulation device 7 is written as b, the field strength E.sub.R of the light transmitted clockwise is given by: ##EQU3## and the field strength E.sub.L of the light transmitted counterclockwise is given by: ##EQU4##
The two light beams having these field strengths are subjected to square-law detection in the light-receiving device 9. The output of the light-receiving device, S(.DELTA..theta., t), is given by: ##EQU5## where D.C. denotes the dc component, and .omega. is the number of vibrations of light waves, with 2.omega. representing a component having twice the number of vibration .omega.. Such a fast signal cannot be detected by the light-receiving device 9 and hence is zero. The output signal from the light-receiving device 9 contains the phase-modulated component .phi., so the phase difference .DELTA..theta. can be determined in association with the amplitude of the modulation signal.
If the dc component is eliminated, S(.DELTA..theta., t) can be rewritten in the form of a sum as follows: ##EQU6## This can be expanded in terms of Bessel functions. By the expansion of the generating function of Bessel functions, we obtain: ##EQU7## If t=exp i.theta., we obtain: ##EQU8## By expanding the real and imaginary parts of equation (9), Ss which is the sine part of S(.DELTA..theta., t) and Sc which is its cosine part can be expanded into series. We define as follows; ##EQU9## By performing conversion .theta..fwdarw..theta.+.pi./2 and using the well known nature of Bessel functions, i.e., EQU J.sub.-n (X)=(-).sup.n J.sub.n (X) (11)
(where n is a positive integer), together with the following substitution: ##EQU10## We obtain: ##EQU11## By equations (13) and (14), the signal S(.DELTA..theta., t) can be rewritten as follows: ##EQU12## This is the expansion of the modulation frequency .OMEGA. by harmonic waves. A desired harmonic component can be obtained by passage through a filter. If the first-order term of the expansion is designated the fundamental component P and the second-order term designated as the second harmonic component Q, the following equations can be obtained: EQU P (t)=2 E.sub.o.sup.2 J.sub.1 (.xi.)cos.OMEGA. t sin .DELTA..theta.(16) EQU Q (t)=2 E.sub.o.sup.2 J.sub.2 (.xi.)cos 2.xi.t cos .DELTA..theta.(17)
In most cases, the fundamental component P is detected to determine .DELTA..theta.. To attain a maximum sensitivity for P, J.sub.1 (.xi.) is maximized. To this end, the modulation index is set in such a way that .xi.=1.8. In this case, J.sub.0 (.xi.) is about 0.3.
The foregoing description concerns the basic construction of a phase modulated fiber-optic gyroscope operating.
When determining .DELTA..theta. by detecting the fundamental component P, the modulation index .xi. must be held constant. Otherwise, the value of J.sub.1 (.xi.) will fluctuate. A method heretofore proposed for maintaining a constant value of modulation index consists of monitoring the second harmonic component Q to determine the value of J.sub.2 (.xi.). This method is described in Japanese Patent Application No. 59-244641. Signal .OMEGA. and signal 2.OMEGA. which is an integral multiple of that signal are picked up from the drive circuit of a phase modulation device. The output of a light-receiving device is subjected to synchronous detection on the basis of these two signals. The detected output is passed through a low-pass filter to obtain a low-frequency component. The second harmonic component Q is: EQU Q=2 E .sub.o.sup.2 J.sub.2 (.xi.) cos.DELTA..theta. (18)
Since the modulation index .xi. must be held constant, the phase modulation device is controlled in such a way that Q is constant. In other words, .xi. is controlled to become 1.8. When .xi. is 1.8, J.sub.2 is about 0.3. If .xi. becomes greater than 1.8, J.sub.2 increases and vice versa. Hence, .xi. can be adjusted to 1.8 by holding constant.
If the quantity of light from the light-emitting device is constant, .DELTA..theta. can be immediately determined from P(t) obtained by equation (16). In practice, however, the amplitude of the light, E.sub.0, will fluctuate, so apparently different outputs will be produced for the same value of .DELTA..theta. on account of fluctuations in the quantity of the light.
For the sake of simplicity, the foregoing discussion assumes that the two light beams, one transmitted clockwise and the other transmitted counterclockwise, have the same amplitude E.sub.0. But this is not the case in practical situations. If it is necessary to distinguish the amplitudes of the two light beams, the amplitude of the light transmitted clockwise is written as E.sub.1 and that of the light transmitted counterclockwise is written as E.sub.2. In other words, the square of E.sub.0 appearing in the previous discussion should be read E.sub.1 E.sub.2.
JP-A-60-135816 (the term "JP-A" as used herein means an "unexamined published Japanese patent application") proposes a control system that provides a constant dc component in output signal. But the problem associated with the quantity of reflected light is not discussed in this patent. By the term "reflected light" is meant those components of light which are reflected from the edge faces of lenses, fiber and other parts of the optical system. These components will not contribute to the measurement of angular velocity but simply become noise. In contrast, signal light passes through the sensor coil and contributes to the measurement of angular velocity.
The light-receiving device receives both signal light and reflected light. The reflected light does not pass through the sensor coil. The control system described in JP-A-60-135816 assumes either the absence of reflected light or the presence of reflected light that will vary in the same way as does the signal light. Only in that case is valid the statement that holding the dc component constant is equivalent to controlling the amplitude of the light to be constant. In practice, however, a quantity of reflected light that is by no means negligible is launched into the light-receiving device. Reflected light will not fluctuate in the same way as does the signal light, or one may say that it will hardly fluctuate. The phase modulation index will also sometimes fluctuate. Therefore, holding the dc component constant does not necessarily result in a constant amplitude of the signal light.
As already mentioned, the prior art fiber-optic gyroscope suffers the problem that substantial variations occur in the quantity of light that is issued from the light-emitting device to be launched into the optical fiber cable. In other words, substantial variations can occur in the amplitude E.sub.0. Thus, apparently different outputs will be produced for the same angular velocity on account of these variations in the quantity of light.
JP-A-61-147106 proposes a control system that is capable of maintaining a constant level of the dc component in the signal. JP-A-60-135816 already cited above proposes that the effects of variations in the quantity of light be cancelled by dividing the phase-modulated frequency component of the signal by the dc component. A phase-modulated fiber-optic gyroscope that operates with the second harmonic component controlled to be constant has also been proposed (see the already cited Japanese Patent Application No. 59-244641). The second harmonic component contains J.sub.2 (.xi.) and holding it constant was considered to be equivalent to controlling the phase modulation index to become constant. However, holding the dc component constant is by no means equivalent to controlling the quantity of light to be constant. The dc component contains .DELTA..theta. in the form of cos.DELTA..theta.. The invention described in Japanese Patent Application No. 59-244641 adopts the approximation of .DELTA..theta..perspectiveto.0 and controls the dc component to become constant on the assumption that it is proportional to the intensity of the light issuing from the light-emitting device. However, .DELTA..theta. sometimes has such a great magnitude that it cannot be neglected. If .DELTA..theta. is substantial, the approximation of .DELTA..theta..perspectiveto.0 will produce inaccuracies.
The approach of maintaining a constant value of the second harmonic component in order to hold the phase modulation index constant has the following problems.
As equation (17) shows, the second harmonic component has not only the J.sub.2 (.xi.) term but also the cos.DELTA..theta. term. The second harmonic component is held constant on the basis of the approximation that .DELTA..theta. is nearly equal to zero. However, this approximation is by no means exact if .DELTA..theta. is great. This will eventually result in failure to maintain a constant value of the phase modulation index.
Dividing the fundamental component by the dc component will cause the following additional problems. The dc component D of the light of interference which is the output of the light-receiving device can be written as: ##EQU13## where H is the quantity of reflected light. If the modulated frequency component in equation (16) is eliminated and if E.sub.0.sup.2 is rewritten as E.sub.1 E.sub.2, the fundamental component P is given by: EQU P=2 E.sub.1 E.sub.2 J.sub.1 (.xi.)sin.DELTA..theta. (219)
In order to obtain correct results by dividing the fundamental component by the dc component, the following assumptions must be taken into account in addition to the problem of reflected light:
Assumption 1: There are no variations in the ratio of the quantity of the light transmitted clockwise to the quantity of the light transmitted counterclockwise;
Assumption 2: There are no variations in the phase modulation index.
If assumption 1 holds, EQU E.sub.2 / E.sub.1 =K (220)
The dc component D can be rewritten as: ##EQU14## where the quantity of reflected light H is neglected. By dividing the fundamental component P by the dc component D, we obtain: ##EQU15## and the resulting output is independent of the quantity of the light emerging from the light-emitting device. Since K and J.sub.0 (.xi.) are known, .DELTA..theta. can be determined. However, this relationship is established only when the above-mentioned assumptions hold and they are impractical.
Further, determination of .DELTA..theta. from equation (222) involves quite complicated mathematical operations. This equation is by no means simple to deal with. One should also remember that the foregoing discussion disregards the quantity of the light inherent in the dc component.